Viviani’s Theorem (VIDEO!)

Pick a point inside an equilateral triangle and sum its three distances to each of the sides of the triangle. Then this sum has value the height of the triangle, no matter the point initially chosen.

This charmer is attributed to 17th-century mathematician Viviani. Here we prove the result, and then go further and let the point wander outside the triangle, and then go to shapes other than triangles!

Viviani’s Theorem


    QUADRATICS, Permutations and Combinations, EXPLODING DOTS, and more!

    Written for educators - and their students too! - this website, slowly growing, takes all the content Tanton has developed in his books, videos, and workshops, and organizes it into short, self-contained, and complete, curriculum units proving that mathematics, at all points of the school curriculum, can be joyous, fresh, innovative, rich, deep-thinking, and devoid of any rote doing! Let's teach generations of students to be self-reliant thinkers, willing to flail and to use their common sense to "nut their way" through challenges, to assess and judge results, and to adjust actions to find success. (Great life skills!)


  • Books

  • Get in touch